Chapter 13
Savings, Capital Formation and
Comparative Economic Growth
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Chapter 13: Savings, Capital Formation
and Comparative Economic Growth
• Savings, investment and economic growth
• The Solow–Swan model of economic growth
• Recent developments in the study of economic
growth
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Saving, Investment and Capital
• Saving frees resources for investment, both public
and private
• Investment adds to the capital stock
• A greater capital stock raises labour productivity
and GDP per capita
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Investment and GDP per capita
13–4
The Solow–Swan Growth Model
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Also referred to as ‘Neo-classical Growth Model’
Gives primary role to saving and capital formation
Minor role to total factor productivity
‘Growth’ refers to growth in output per worker,
which by implication extends to growth in GDP per
capita
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The Production Function Again
• Y = Af (K, L)
• Rewrite this function in ‘per worker’ terms by
dividing both sides by L
• Y/L = y = Af (k) where k = K/L
• GDP per worker rises with the stock of capital per
worker
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Diminishing Returns to k
• Diminishing returns to capital accumulation apply
• The higher is the existing capital–labour ratio (k),
the smaller is the increase in GDP per worker (y)
when there is an increase in k
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Capital–Labour Ratio and Output
13–8
Are There Limits to Growth?
• Yes, because at some point the capital stock
becomes so large that all of the economy’s saving
is devoted to equipping new workers at the
existing capital–labour ratio, and to replacing that
part of the capital stock which wears out, rather
than to increasing the stock of capital per worker
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Three Types of Investment
• Physical capital wears out through depreciation
and needs to be replaced by ‘replacement
investment’
• This form of investment needs to be distinguished
from ‘new or net investment’ which refers to the
investment over and above replacement which
increases the size of the capital stock
• Gross Investment = Net Investment +
Replacement Investment (Depreciation)
• Net Investment = Gross Investment – Depreciation
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‘Investment’ in Growth Models
• In growth models, the terminology is slightly
different
• ‘Replacement investment’ also includes the
amount of new investment which is required to
equip new workers with the same capital as
existing workers
• ‘New investment’ refers to investment which
increases the capital–labour ratio, k
• ‘Gross investment’ is said to be zero when the
capital–labour ratio is constant, even though the
stock of capital has increased
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Two Claims on Saving
• Before there can be net investment – an increase
in capital per worker – and further growth, saving
must be sufficient to meet two claims on it
– First, new workers have to be equipped with enough
capital that the capital–worker ratio does not fall
– Second, a fraction of the capital stock which wears
out (depreciates) each year and must be replaced
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Requirements for Growth
• When these two claims are just met by saving, the
stock of capital per worker, k, remains constant:
net investment is said to be zero and output per
worker, y, remains constant
• When saving exceeds these two claims, k can
increase: net investment is is said to be positive
and y rises
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First Requirement for Constant k
• Suppose the existing capital–labour ratio is k
• To maintain a constant k in the face of growth in
the labour force, the capital stock must grow at the
same rate as the labour force, say n.
• This requires an increase in the capital stock of nK
• This is because, if Δ/K = n, Δ = nK, where Δ means
the change in the capital stock
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Second Requirement
• Let the fraction of the capital stock which wears
out be d
• So the required replacement investment is dK
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Total Requirements
• In the face of an increase in the labour force and
depreciation, the gross investment which is
required to maintain a constant capital–labour ratio
is (n + d)K
– nK to equip the entrants to the labour force
– dK to offset depreciation
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Saving Puts a Ceiling on k and y
• Saving S finances replacement and net investment
• S = sY, where s is the average propensity to save
• Growth continues whenever the capital–labour
ratio increases: when sY > (d + n)K
• Growth ceases whenever the capital–labour ratio
remains constant: when sY = (d + n)K
• At this point there is zero net investment, and the
capital–labour ratio and labour productivity are
both constant
• The economy is in a ‘steady state’
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Meaning of the ‘Steady State’
• Capital per worker, k, is constant so that output per
worker, y, is also constant
• Below the ‘steady state’ k is rising so that y is also
rising
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The Path to the ‘Steady State’
13–19
Going Backwards
• An economy could lie beyond its steady state if the
rate of growth of the labour force had accelerated,
so that saving was now inadequate to equip new
workers with the same capital as existing workers
• The capital labour ratio and income per capita
would fall back to the steady state
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Going Backwards
13–21
Implications of the Steady State
• An end to growth in living standards
• Convergence of living standards between rich and
poor countries – but only if they have the same
production functions and the same rates of saving
and long-run labour force growth
• Poor countries will grow faster than those richer
countries which have reached their steady state
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When is there Convergence?
• We need to compare countries with similar labour
force growth rates and with similar production
functions and degrees of ‘open-ness’ to the rest of
the world
• Convergence is ‘conditional’
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Evidence of Convergence
• For high-income countries, there is an inverse
relationship between the level of income and the
growth rate
• This means that, among these countries, the
relatively poorer ones are ‘catching up’ to the
richer ones
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The Rich Converge
13–25
Convergence and Openness
• Open economies tend to converge
• This is because their openness allows them to
influence each others’ economies
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Convergence and Openness
13–27
The World Is Not Converging
13–28
Solow–Swan Model Just a Start
• Steady state not yet observed for rich countries
• Growth accounting tells us that investment and a
rising capital–labour ratio are not the main
ingredients in growth of living standards
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Endogenous Growth Models
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Key role for raising total factor productivity (TFP)
Role of education and human capital in TFP
Role of research and development (R&D) in TFP
Role of patent protection in R&D
Protection of property rights in general
Role of political structure in protecting property
rights and punishing policy failures
• All these factors are inter-related
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